An apparatus of this kind is the subject matter of an earlier invention of mine disclosed in German laid-open application No. 28 05 801. In that case, the drum is provided on its inner cylindrical surface with guide baffles having aerating holes on a small area while additional air circulation is facilitated by laterally perforated hollow blades disposed at the frustoconical end walls thereof. Since, apart from the guide baffles and blades, all surfaces bounding the interior of the drum are centrally symmetrical about its axis of rotation, the granules are not strongly entrained during the tumbling process so that their lower strata tend to slide down along the drum wall. The coating of the granules is thereby subjected during hardening to increased wear under locally nonuniform stress whereby an uneven thickness results. The coating can therefore protect the granules only to an insufficient degree since the efficiency of protection is determined by the thickness of the covering layer at its weakest spot. The uniformity of the layer thickness is particularly important in the case of thin-walled capsules for liquid active agents in the pharmaceutical industry.